Study On The Ellipse Question-solving Mistakes Of High School Seniors

Conic curve is a core part of analytic geometry.It is the major approach to study conic curve that students apply algebraic method to solve geometric problems.Senior three students have trouble with conic curve.This paper mainly studies the error types,the error-prone points,error causes and measures to reduce errors in solving elliptic problems of senior three students.Firstly,the author analyzes relative literature on problem solving errors.With Newman's error analysis framework,the thesis divides problem solving errors into five types: reading error,understanding error,conversion error,operation error,and coding error.By testing students and interviewing students and teachers with typical errors after the test,the error types and error-prone points of elliptic problem solving errors are analyzed,paving the way for subsequent research on the causes of elliptic problem solving errors.It is found that the most frequent error type in ellipse solving is operation errors,accounting for 38%.And the other error types comprise 34%conversion errors,16% understanding errors,and 12% coding errors.There is no reading error.Students are apt to make mistakes in four aspects.(1)Students cannot apply the definitions proficiently.(2)The focus position is not discussed in solving the standard elliptic equation.(3)When calculating the range of eccentricity of ellipses,the exact inequality cannot be found.(4)It is easy for students to make mistakes in obtaining quadratic equations with one variable when they eliminate linear and elliptic equations simultaneously.Secondly,with the aid of Likert scale,the author made a questionnaire "A Survey on the Causes of Elliptic problem solving errors of Senior Three students",and conducted the survey among 220 students from a middle school in Lanzhou,Gansu Province.Excel was used to conduct data statistics on the original data,and SPSS was used to conduct data analysis,including descriptive analysis,reliability,validity and factor analysis of the questionnaire.Then the thesis analyzes the causes of students' errors in elliptic problem solving from the five dimensions of "four bases and four abilities",core literacy,mathematics learning habits,"emotion,attitude" and other aspects.It is found that the main causes of students' error in elliptic problem solving are :(1)emotion,attitude and learning habit,(2)cognitive,thinking and psychological reasons,(3)the reasons for the treatment of wrong questions,(4)objective reasons,(5)"Four basic,four ability",discipline core accomplishment.At the same time,the author also learned the reasons for students' mistakes and measures to reduce mistakes through interviews with teachers.Finally,based on the feedback of questionnaire survey and interview,the author proposed some measures to reduce errors for senior three students and teachers.For students,there are four measures.(1)Strengthen the grasp of basic knowledge and the understanding of core concepts.(2)Improve mathematical operation literacy.(3)Enhance error management methods.(4)Boost self-confidence and solve problems in a clam manner.There are three measures for teachers.(1)Study the teaching materials and make proper use of modular teaching.(2)Adopt a more targeted way to deal with the wrong questions.(3)Emphasize and attach importance to the standard of blackboard writing.Hope these measures can help students reduce problem solving errors,improve their thinking process,improve their problem solving ability,and develop the core literacy of the subject.